Why isn't the ElliotSig activation function widely used?
I can't speak for individual researchers, but I can guess why the community as a whole hasn't adopted this activation function.

ReLU is just so incredibly cheap. This benefit continues to grow as networks grow deeper. Also, they work reasonably well. As pointed out in Searching for Activation Functions, 


  the performance improvements of the other activation functions tend to be inconsistent across different models and datasets.


Even if a new activation function did provide a meager improvement in performance across the board, I wouldn't be surprised if ReLU were still commonly used. It's the default for a lot of machine learning software already.

Also research isn't ordinarily about eeking out one more percentage point in accuracy on a specific task. If I were entering in a competition, I might experiment with activation functions. But even then I'd rather use ReLU and save a little time while prototyping my architecture.

As pointed out by @DuttaA in comments, softsign could potentially replace sigmoid and tanh in situations where a bounded output is desired. I haven't seen anyone compare them before, but softsign would at least be much faster. I'm guessing this replacement hasn't happened because of tradition and exposure. Not because of softsign's lack of infinite derivatives. I don't know if this happening would make softsign "widely used", but it would be something.